Verified calculation capability

Numerical interpolation Calculation Capability

Piecewise-linear, Lagrange, or natural cubic spline of tabulated (x, y). Not regression, not CAS. · Math · Numerical

Capability ID math.numerical.interpolate · version 1.1.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Linear

Linear: y = y₀ + (y₁−y₀)(x−x₀)/(x₁−x₀)
Lagrange: y = Σ yⱼ ℓⱼ(x), ℓⱼ = Πᵢ≠ⱼ (x−xᵢ)/(xⱼ−xᵢ)
Natural spline: S″(x₀) = S″(xₙ) = 0

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`method`	—	—	input / output
`x`	Abscissa at which to evaluate y.	—	input / output
`points`	x,y; x,y pairs (semicolon-separated)	—	input
`x0`	—	—	input
`y0`	—	—	input
`x1`	—	—	input
`y1`	—	—	input
`extrapolate`	If true, linear and spline use the end piece outside [x_min, x_max].	—	input
`y`	—	—	output
`n`	amount of substance	—	output
`x_min`	—	—	output
`x_max`	—	—	output
`in_range`	—	—	output
`extrapolated`	—	—	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

Assumptions

Unique x; sorted internally
Natural spline ends, not clamped
Not Akima / PCHIP / regression / CAS

Example

One numerical check. The calculator page holds worked steps and FAQ.

linear (0,0)(10,20) x=5 → 10

Open this example in the calculator

Trust

Review-policy: engine tested — automated tests, sources, version lock, and evidence published. Supplemental to CVP; not Domain Expert Review. See CVP and Review policy.

Tier: Engine tested — catalog token engine_tested
Calculation version: 1.1.0
Evidence tests: 13/13 calculation tests · golden 4/4 · boundary 2/2 · property 7/7
Engine tested: Yes
Source checked: Yes
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.1.0 (workspace artifacts agree)

Production attestation: Embedded snapshot: unpublished · Build schema 1.1.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (1 capability; 163 remain CURRENT) @ 2026-09-19T00:00:17.039Z
Semantic contract: PASS
Evidence attested at: 2026-09-18T21:41:55.460Z
Last production check: 2026-09-18T21:41:55.460Z
Public / cache: —
Origin: —

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 4/4.

Tool id: numerical-interpolation
Engine: numerical-interpolation
REST: POST /api/v1/calc/numerical-interpolation
MCP: execute_calculation with capability_id: "math.numerical.interpolate"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.1.0)
Versioned output schema: Immutable pin (1.1.0)

References

Human-readable sources plus CVP reference evidence classes.

Sources

ISO 80000-2:2019 Quantities and units — Mathematics

Try with an agent

Inspect this capability via same-origin MCP, then call execute_calculation.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"math.numerical.interpolate"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.1.0) when reproducibility matters. Full protocol notes: MCP docs.